Meander, Folding and Arch Statistics

The statistics of meander and related problems are studied as particular realizations of compact polymer chain foldings. This paper presents a general discussion of these topics, with a particular emphasis on three points: (i) the use of a direct recursive relation for building (semi) meanders (ii) the equivalence with a random matrix model (iii) the exact solution of simpler related problems, such as arch configurations or irreducible meanders.Comment: 82 pages, uuencoded, uses harvmac (l mode) and epsf, 26+7 figures include

Flexible and stretchable circuit technologies for space applications

Flexible and stretchable circuit technologies offer reduced volume and weight, increased electrical performance, larger design freedom and improved interconnect reliability. All of these advantages are appealing for space applications. In this paper, two example technologies, the ultra-thin chip package (UTCP) and stretchable moulded interconnect (SMI), are described. The UTCP technology results in a 60 µm thick chip package, including the embedding of a 20 µm thick chip, laser or protolithic via definition to the chip contacts and application of fan out metallization. Imec’s stretchable interconnect technology is inspired by conventional rigid and flexible printed circuit board (PCB) technology. Stretchable interconnects are realized by copper meanders supported by a flexible material e.g. polyimide. Elastic materials, predominantly silicone rubbers, are used to embed the conductors and the components, thus serving as circuit carrier. The possible advantages of these technologies with respect to space applications are discussed

Meanders: A Direct Enumeration Approach

We study the statistics of semi-meanders, i.e. configurations of a set of roads crossing a river through n bridges, and possibly winding around its source, as a toy model for compact folding of polymers. By analyzing the results of a direct enumeration up to n=29, we perform on the one hand a large n extrapolation and on the other hand we reformulate the available data into a large q expansion, where q is a weight attached to each road. We predict a transition at q=2 between a low-q regime with irrelevant winding, and a large-q regime with relevant winding.Comment: uses harvmac (l), epsf, 16 figs included, uuencoded, tar compresse

Limit laws for discrete excursions and meanders and linear functional equations with a catalytic variable

We study limit distributions for random variables defined in terms of coefficients of a power series which is determined by a certain linear functional equation. Our technique combines the method of moments with the kernel method of algebraic combinatorics. As limiting distributions the area distributions of the Brownian excursion and meander occur. As combinatorial applications we compute the area laws for discrete excursions and meanders with an arbitrary finite set of steps and the area distribution of column convex polyominoes. As a by-product of our approach we find the joint distribution of area and final altitude for meanders with an arbitrary step set, and for unconstrained Bernoulli walks (and hence for Brownian Motion) the joint distribution of signed areas and final altitude. We give these distributions in terms of their moments.Comment: 33 pages, 1 figur